Download SPH3U: Forces, Mass and Motion

Forces
Day Lesson
Topics
In Class
Homework
65
What is a Force?
Idea of force
Elastics, spring scales
66
What is the Effect of a
Force?
Force causes
acceleration
67
What are the Effects
of Many Forces?
Combining forces,
net force
68
Free Body Diagrams
Newton’s 1st law,
free body diagrams
Dynamics carts, elastics
spring scales, tickertape
timer
Dynamics carts, spring
scales
Double Atwood machine
demo
Develop 1st law
Hover-puck demo
Video: Fundamental Forces
Assign Song / Video Project
Video: Feynman and Inertia
69
The Force of Gravity
&
Normal Force
Force of gravity,
gravitational field
strength, Fg = mg
Normal force
Take up FBD Howo
Masses, spring scales
Metersticks, masses, spring
scales
70
Force, Mass and
Motion
Force, Mass and
Motion – part 2
Newton’s Second
Law Problem Solving
Force and mass
affect acceleration
Newton’s 2nd law,
Fnet = ma, definition
of force, definition
of Newton, inertia
Force problem
solving techniques
Dynamics carts, masses,
tickertape timers, pulleys
Finish activity
71
Forces as Interactions
Newton’s 3rd law
Forces are
interactions
Newton’s 3rd Law,
Force pairs
Two carts on track
Computer force probes,
two carts on track
Develop Newton’s 3rd Law
72
Friction
Kinetic and static
friction
Coefficient of
friction, Ff = Fn
Friction boxes, masses,
spring scales
Finish activity
Friction problem solving
73
Gravity
Orbit, tides,
universal
gravitation
74
Review
75
Test
Develop 2nd law
Video: Inertia Hip-Hop
Read: “Newton’s First Law of Motion”,
pg. 59-63
Handbook: Homework – Free Body
Diagrams
Video: First Law
Video: Forces in Space!
Read: “Gravitational Force on Earth’s
Surface”, pg. 84-88
Problems: pg. 85 #2-5, pg, 86 #6-8, pg.
87 #10
Video: Big Bang Theory
Video: Gravity – Newton to Einstein
Read: “Forces we Experience Daily”,
pg. 55-56
Problems: Homework – Normal Forces
Video: Normal Force
Video: Normal Force
Video: Cars and Inertia
Read: “Newton’s Second Law of
Motion”, pg. 71-73
Problems: pg. 73 #1,2,4,6
Lesson: Newton’s Second Law
Video: 2nd Law in Space!
Problems: finish handbook questions
and pg. 81 #16
Lesson: Finding the Net Force
Video: Misconceptions About Freefall
Video: 3rd Law in Space!
Video: Newton’s Third Law
Read: “Newton’s 3rd Law of Motion”,
pg. 74-77
Problems: Homework – Newton’s Third
Law
Read: “Effects of Friction”, pg. 96-103
Video: Brake Test
Video: Chevy Volt Test
Problems: pg 97 #1, pg. 100#1, pg. 103
#3,4,5,6 pg. 105#7
Lesson: Static and Kinetic Friction
Lesson: Friction Problem
R+MN 3.1 P#2,3,4,5,9*,10,11 Q#2,9
3.2 P#3,4,5,7,9 Q#1,2
Review: Newton’s Laws
Problems: pg. 107 #1,2,5,
Chpt 2 Rev #2,3,4,7,10,11,12,14,16
Chpt 3 Rev #6-10,14-16
Unit 1 Review # 13,20,22,24,25,26
Representations of Forces and Motion
1
SPH3U: What is a Force? – Day 65
A: What is force?
Force is a commonly used word in everyday speech. Our goal is to
understand the scientific role of force in the workings of our world!
Recorder: _________________
Manager: _________________
Speaker: __________________
0 1 2 3 4 5
1. Describe what a force is as if you were talking to a friend’s younger brother or sister. Give some suitable
examples of forces.
B. Units of Force
Make sure every member of your group tries this activity! You will need: 3 identical elastics, a 20 N spring scale,
and a ruler.
1. Loop one elastic around your two pointer fingers. Separate your fingers until the rubber band has a bit of
stretch. You have now created your standard unit of force. Describe a method using the ruler that will allow
other people to create the same amount of force.
2. Give your unit of force a name (often in honour of its discoverer).
3. Describe the feelings of force experienced by each finger while the elastic is stretched. How do the feelings of
each finger compare?
4. Rest your fingers and try it again using two elastics now. Be sure to use the same standard distance. Describe
how the sensation of force has changed. Can you estimate how much has it changed? Explain.
5. One day on a hike you find an interesting, heavy rock. Explain how you could use your collection of elastic
bands and your method from question B#1 to measure the weight of the rock.
* Check your answers with your teacher before continuing.
2
C. Measuring Force
Rather than carry around a bag of elastics and ruler, we will use a spring scale to measure the size of forces.
Before you get your license to operate a spring scale, you need to know how to calibrate it. Hold the scale
horizontally or vertically, just as you will use it when measuring, but without pulling on the hook. Adjust the scale
(a sliding cover or nut at the top) so it reads zero. The scale reads in units called newtons.
1. Why is it important to hold it with the same orientation as you would when making your measurement?
2. Create your standard unit of force but replace one finger with a spring scale. What is your unit of force
equivalent to in newtons?
3. Make a prediction: When you replace the second finger with a second spring scale (and hold the elastic to its
standard length), what will each scale read?
4. Now actually replace the second finger with a second spring scale and note the readings. Offer an explanation
for any differences with your prediction and try to explain why the readings are they way they are. (This is
related to how strings and ropes work.)
5. In question B#4 you used two elastics and described how the feeling of the force changed. Test this situation
with one spring scale. Does the result agree or disagree with the sensation you experienced? Justify your
answer.
6. Predict the size of the force three elastics stretched to your standard length would exert. Explain.
7.
Measure the force exerted by three elastics. Explain any discrepancies between your prediction and
measurement.
8. Describe how you could create your own (and maybe different) markings on the spring scale if all the
numbers and lines rubbed off!
9. In this activity we combined two and then three equivalent forces from the elastics and measured the results
with the spring scale. Describe a general rule for determining the total effect of a number of equivalent forces
acting together. (We will develop this into a very powerful rule!)
3
SPH3U: What is the Effect of a Force? – Day 66
Recorder: _________________
Manager: _________________
Speaker: __________________
What happens when a single force acts on an object? This is a tricky
question that took very clever people about 2000 years to answer. Now
0 1 2 3 4 5
it’s your job to figure it out! (Don’t worry - it won’t take as long this time
around.) In all the examples that follow, we will be examining the effect of a single, constant force.
A: The Steady Pull
1. Prediction: Describe how the dynamics cart would move if it experiences a constant horizontal force (a
steady push or pull).
2. Get a dynamics cart, some masses, an elastic and ruler. Determine a technique that will allow you to exert a
constant force on the dynamics cart using these materials. You should be able to do this for an interval of
about four seconds (this is why the masses may be necessary). Take your time doing this. (Hint: Think back
to the activity from last class.)
3. Describe what a skeptical person would observe that should convince them the cart is experiencing a steady
force.
* Practice your technique until you are good at it! Demonstrate this for your teacher before going on.
4. Prediction: Revise your prediction from question A#1, if necessary, based on what you have observed.
Predict what the v-t graph and tickertape dot pattern for the dynamics cart might look like.
v
t
Get a tickertape timer and attach one metre of tickertape to the cart. Practice pulling your cart with a steady force
through the timer a few times before turning the timer on!
5. Examine the pattern of dots on the ticker-tape. Why might the dots near the very beginning and end be less
reliable?
6. Draw a sample of the ticker-tape dot pattern below, only while the cart experienced a constant force. Describe
the motion. Explain how this data supports or contradicts your prediction from question A#4.
4
B: Release the Cart!
Pull the cart along the floor, allow it to speed up and then release it. All of the questions in part B will be about
the cart’s motion after it is released.
1. Describe the motion of the cart after it has been released.
2. A student says, “Once the cart is released, it comes to rest on its own. There are no longer any forces acting
on it – it just slows down by itself because we’re not pushing on it anymore.” Agree or disagree with the
student. Explain your reasoning.
3. Describe how the motion of the cart would be different if we could smooth out the floor to reduce friction a
bit.
4. Imagine we very carefully remove all sources of friction. What would we observe in this very special
situation after the cart is released? In this situation what horizontal forces are acting on the cart?
C: Conclusions – Forces and Motion
Complete the chart below based on today’s observations and your conclusions. This will become an important
rule about the effects of forces!
Situation
Resulting Motion
One single, constant force
No forces at all
(two possibilities!)
1)
2)
1. Two students discuss today’s activities. Do you agree with either student? Explain.
Student 1: “The cart experiences friction all the time, even during Part A. But we said there was
only one force, the one from our elastic. This means our conclusions might be wrong.”
Student 2: “I agree there was friction. We also saw in Part B that it took friction a long time to
stop the cart. That means it’s a much smaller force than the pulling force. So maybe we can say
that there was only one important force acting on the cart in the first activity.”
2. The two students are still discussing. Do you agree with either student? Explain.
Student 2: “Wait a minute. I bet there were other forces, vertical ones like gravity. Gravity is
pretty strong so maybe that will ruin our conclusions. Still no single force!”
Student 1: “Well, we didn’t see the cart move downwards at all, so it looks like gravity is not
having an effect on the cart’s motion. So there was only one horizontal force. I think our
conclusions are still fine.”
5
SPH3U: What are the Effects of Many Forces? – Day 67
A car driving down the road experiences many forces at the same time.
What happens in such a case? In this activity you will find out. You will
need: a dynamics cart, a heavy mass, and three identical spring scales (5
or 10 N). Throughout this activity friction is very small compared to the
other forces involved and therefore its effects can be ignored.
Recorder: _________________
Manager: _________________
Speaker: __________________
0 1 2 3 4 5
A: One Single Force
Place the mass on the dynamics cart and exert a
steady 2 N horizontal force using a spring scale.
Spring scale
1. Describe the motion of the cart.
To help us understand the effects of forces, we introduce a new tool called the free-body diagram (FBD). We
simplify the object in question by modeling it as a point. Next, we draw a vector arrow, starting at that point, for
each force the object experiences. The length of the arrow is not important, but it is helpful if their relative size is
roughly correct.
2. Draw a FBD for the cart showing the horizontal forces. Label your force using the vector symbol
.
B: Two Forces
Exert two equal forces on
the cart, but in opposite
directions.
+ x- direction
Spring scale
Spring scale
1. Describe the motion of the cart. Record the size of the forces.
2. Draw a FBD showing the horizontal forces. Label the forces
and
.
3. Describe the total effect of the two forces on the cart.
We can mathematically represent the total effect of the two forces by defining a new quantity called the net force,
which is the sum of the forces acting on the object.
4. Fill in the vector equation and find the net force. Be sure to indicate the direction of each force.
________ + ________ = ________
6
An alternative and convenient way (and the one we will use) to find the net force is by changing the vector
equation into a scalar equation. Use the sign convention indicated in the diagram above. Forces acting in the
positive x-direction are labelled positive and forces acting in the negative x-direction are labelled negative. The
values of the force symbols are all positive.
5. Complete the scalar equation below and find the net force.
= ______ N - ______ N = _______ N
When the net force equals zero we say that the forces acting on the object are balanced. In part B the horizontal
forces acting on the object are balanced.
* Check your results with your teacher before continuing.
C: Net Force Zero
The example in Part B demonstrated that an object initially at rest that experiences a net force of zero will remain
at rest. What will happen to an object that is already moving which experiences a zero net force? This is a class
demonstration your teacher will lead.
1. Draw a FBD for the cart your teacher has set up. Note that the strings attached to the weights are pulling on
the cart horizontally. Use the force values your teacher gives you.
2. Write an expression for the net force and calculate the result.
Your teacher will start the cart moving and then let go. Once released, the only horizontal forces acting on the cart
will be those provided by the strings.
3. Prediction: How will the car move after being released?
4. Describe your observations. Do they confirm your prediction? Explain.
D: Net Force is Not Zero
This is another class demonstration. The only difference with the pervious is that one of the weights is smaller.
1. Draw a FBD and label the two forces. Use the values your teacher gives you.
2. Write an expression for the net force and calculate the result.
If the net force is not equal to zero, we say that the forces acting on the object are unbalanced.
3. According to your calculation, what single force would the effect of the two forces be equivalent to? Explain
why this is reasonable.
7
4. Prediction: How will the car move after it is released?
5. Describe your observations. Do they confirm your prediction? Explain.
E: Three Forces!
It is now time to return to your dynamics cart. Your challenge is to use three spring scales on your cart to show
that two, 2 N forces balance a single 4 N force. (Make sure all your scales are pulling along one line)
1. Draw a diagram showing the configuration of the cart and scales.
2. Explain why you believe your set-up demonstrates the given condition.
3. Draw a FBD and label the three forces.
4. Write an expression for the net force and use your values to calculate the result.
5. What evidence have you seen today that justifies our use of vector quantities to describe forces? Explain.
F: Conclusions – Forces and Motion
Complete the chart below based your understanding of forces and your observations thus far.
Situation
Net Force
(circle one)
Resulting Motion
No forces at all
zero / non-zero
1)
2)
Balanced forces (two
or more)
zero / non-zero
One single,
unbalanced force
Unbalanced forces
(two or more)
zero / non-zero
1)
2)
zero / non-zero
1. Which situations above produce the same kinds of motion? What property do they have in common?
2. Devise a rule that relates the net force with the resulting motion.
8
SPH 3U: Representing Forces – Free Body Diagrams – Day 68
A free body diagram (FBD) is a tool that helps us understand the total effect
Recorder: __________________
of all the forces acting on an object. There are a few steps that you should
Manager: __________________
always go through when you draw a FBD.
Speaker: __________________
 Model the object as a point-particle
0 1 2 3 4 5
 Represent the external forces acting on the object using vectors that
start at the point (the object’s centre of mass). Note: the force vectors do not need to be drawn to scale, but should be
drawn roughly according to their relative magnitudes.
 As a guide, always ask the question: “At this moment in time, what is pushing or pulling on the object?” We are
looking for all the different interactions the rock may be experiencing.
 Include a separate wiggly acceleration vector whenever possible.
 Draw a coordinate system with a sign convention such that the direction of the acceleration is positive.
Common forces: Fg = gravity, Ft = tension (force from string or rope), Fn = normal force (force from contact with another
object), Fa = applied force (a special normal force for people), F f = friction (a force between sliding surfaces)
A: The Falling Rock
Consider the situation shown to the right of a falling rock.
A rock is
falling.
FBD
1. At this moment in time, what is pushing or pulling on the rock?
The Air Resistance Rule: For our purposes, we will always assume there is no air
resistance (Fair) unless it is mentioned or the situation does not make sense without it.
2. Draw the FBD.
The purpose of the FBD is to help us understand the total effect of all the forces acting
on the object. This total is called the net force, Fnet. To calculate the net force, we must add up all the force vectors found on
the FBD.
3. Write a vector equation for the net force the falling rock experiences.


Fnet  F 
Working with a vector equation is often inconvenient. Instead, we construct two scalar equations that represent the forces in
the x- and y-directions. To do this, follow these steps
 Choose a sign convention for the coordinate system with the direction of acceleration as positive.
 Write the scalar equation using the force sign convention.
The Force Sign Convention: When we write a scalar equation involving forces, the force symbols, such as F g, are all
positive quantities. Show the directions of the forces by using a sign convention and adding or subtracting the appropriate
magnitudes. For example: Fnet = Fn – Fw
4. Draw a coordinate system and sign convention for the falling rock. Include this in the box above.
5. Write a scalar equation for the net force in the y-direction. Include this in the box.
B: Terminal Velocity
A rock is falling at a constant speed. This is called the object’s terminal velocity.
1.
Draw a FBD. Write an expression for net force in the y-direction. (Be sure
to follow all the steps!)
2.
Note the motion lines in the diagram. A student asks, “How can the rock be
moving if the acceleration is zero?” Offer an explanation to the student.
A rock is
falling at
terminal
velocity.
FBD
9
C. The Hand Force
A student pushes a cart along a table. The cart leaves her hand, gradually slows down and stops.
FBD
1.
At what moment in time does the force due to the hand stop
affecting the cart? Explain.
2.
The cart travels about two metres before it stops. A students
says, “There must still be a forward force on the cart or else it
would just stop as soon as she lets go.” Do you agree or
disagree? Explain.
3.
Draw a FBD for the rock after it is released, while it is slowing down. Write an expression for net force in the x- and ydirections.
D: Going Up!
A rock is tossed straight upwards. We examine it at a moment in time while it is still
travelling upwards.
FBD
1.
Draw a FBD for the rock while it is moving upwards. Write an expression for
the net force in the y-direction.
2.
A student says, “How can something be travelling upwards when the only force
acting on it is downwards? There must be an upwards force acting on the rock.”
Do you agree or disagree? Explain.
3.
Compare the FBDs and equations from parts A and D. Based on your comparison, what information can we not find
from a FBD.
E. The Finale
A rock is being pulled by a string along a rough surface. It is gradually slowing down.
1.
Draw a FBD for the rock and write
an expression for net force in the xand y-directions.
2.
Compare the magnitudes of the
forces in the horizontal and vertical
directions and explain any
differences.
10
Slowing down on a rough surface
FBD
Homework – Free Body Diagrams
For each situation, draw a complete FBD, write an expression for the net force in the x- and y-directions and
compare the magnitude of the forces whenever possible.
1. The rock has been thrown
upwards and is slowing
down.
2. The rock is at rest.
3. The rock has a book
placed on top of it.
4. The rock is moving
upwards and is slowing
down.

v
5. The rock is tied to a rope
and is at rest.
6. The rock is speeding up
and experiences friction.
7. The rock is being pulled
by two strings. It is not
moving.
8. The rock is tied to a rope
and is being pulled upward
but is slowing down at this
moment in time.
9. The rock is being held
against a wall with a
horizontal force.
10. The rock tied to a rope is
swinging.
11
SPH3U: The Force of Gravity! – Day 69
Question: How does an object’s mass affect the size of the force of
gravity it experiences? You will need: one spring scale, a variety of
masses, and some gravity.
Recorder: _________________
Manager: _________________
Speaker: __________________
0 1 2 3 4 5
1. Draw a FBD for a mass hanging from the spring scale. Explain
why we can use the scale reading (the upwards force or tension) to determine the
size of the force of gravity.
FBD
2. Which quantity is your dependent variable? On which axis of a graph does this
belong?
3. Use the chart below and grid to record and represent your results.
Mass (kg)
Force of
Gravity (N)
0
4. Determine the slope of your graph, including units. Show your work on the graph.
5. Write an equation for your line of best fit – use the symbols Fg and m.
6. Use your new equation to determine the size of the force of gravity acting on a 1.5x103 kg car.
12
SPH3U: The Normal Force – Day 69 cont’d
For these activities you need: two metre sticks, a spring scale and a 500 g
mass.
Recorder: _________________
Manager: _________________
Speaker: __________________
0 1 2 3 4 5
A: The Mystery Force
Your friend places her backpack on a table and draws a FBD of it which is shown to the right.
You remark that there should be another force, but your friend does not understand why.
1. Convince your friend why another force must be acting on the backpack. Cite direct
evidence about the object that you can readily observe.
2. The backpack has a mass of 5.8 kg (all those textbooks). Predict the size of the additional force. Describe
what object exerts this force on the backpack. Complete her original FBD.
B: The Normal Force
The name for the force we predicted in part A is the normal force. Two objects that are in contact interact and
exert normal forces upon one another. These forces always act perpendicular to the surfaces at the point of
contact. This force usually prevents objects from deforming much, breaking or simply merging together.
1. Give three examples of objects or substances that you think might be able to exert large normal forces and
three that might be able to only exert small or negligible normal forces.
Make a bridge using the metre stick between two tables. Gently press downwards with your finger in the middle
of the metre stick.
2. Describe what you observe happening to the “rigid” metre stick. What force is responsible for the change in
the stick’s shape?
3. Describe the evidence for an upwards force acting on your finger (give one observation and one sensation).
13
We are using metre sticks to model a typical surface, like a table top or wall. Place the 500 g mass on the metre
stick. Note what happens. Remove the mass. Place the second metre stick directly on top of the first (the “table” is
twice as thick) and place the 500 g mass on top of the two sticks
4. What is different about the effect of the mass on our new “table”? Explain.
5. Imagine many, many metre sticks stacked up (a thick table). What would happen to the metre sticks if we
place the 500 g mass on top of them? How has the size of the upwards normal force changed compared to the
one metre stick situation? Explain.
6. Propose a model that describes what happens inside an object in order to produce normal forces. Make a
guess and quickly move on.
C: The Measuring the Normal Force
Rest your hand on the table and place the 500-g mass on the flat palm of your hand.
1. What evidence is there that your hand exerts an upwards normal force on the mass?
2. What evidence is there that the mass exerts a downwards normal force on your hand?
3. What is the size of the normal force on the mass? Explain.
4. Prediction: What will happen to the mass in your hand when another group member exerts
a 4 N force upwards on it? Draw a FBD. How will your hand feel? What will the size of the
normal force be?
5. Attach a spring scale to the mass and exert a 4 N force upwards. How did the sensation in
your hand change? What force or forces do you think have changed size due to the upwards
force?
14
FBD
Homework – Normal Forces
1. A child throws a very bouncy ball which hits a wall and then the ceiling. Draw a FBD for the ball
while it is in (a) contact with the wall and (b) in contact with the ceiling.
2. A 0.5 kg book rests on top of your friend’s outstretched hand.
a) Draw a FBD for the book.
b) Determine the size of the normal force.
Physics
FBD
c) Your friend’s hand begins to move upwards and speed up. How have
the forces on the book changed? Explain.
d) Your friend’s hand is still moving upwards but is slowing down. How have the forces on the
book changed? Explain.
e) The net force is 3.0 N [upwards]. Determine the size of the normal force acting on the book.
3. Your friend places the book on a table and stacks large rock on top of it.
a) How has the upwards normal force of the table on the book changed? The rock has a mass of
1.3 kg. What is the size of this normal force?
b) Does the table exert a normal force on the rock? Explain.
15
Day 70
http://www.walter-fendt.de/ph14e/n2law.htm
Name _____________________
Newton's Second Law of Motion
PURPOSE
In this virtual laboratory activity, you will investigate the changes in the motion of a
dynamics cart that occur when different amounts of net force are applied on a system
with constant mass. You will also investigate the changes in motion that occur when the
applied force is constant, but the total mass of the system is changed.
THEORY
Isaac Newton described the relationship of the net force applied to an object and the
acceleration it experiences in the following way: the acceleration (a) of an object is
directly proportional to and in the same direction as the net force (Fnet), and inversely
proportional to the mass (m) of the object.
Procedure
a
Fnet
m
1. Place about 1.0-gram of mass (0.001 kg) for the initial hanging mass.
2. Set the cart mass to 399-g (0.399 kg).
• The applied net force is the weight of the hanging masses (Fw = mg) minus friction
forces. Set Friction to 0.0-N by setting the coefficient of friction to 0.00.
3. Record the total mass of the cart as "M".
4. Record the total mass of the hanging mass(es) as "m".
5. When you are ready to collect data, press the "start" button.
6. Record the measured acceleration from the screen display in the data table and notice
the plotted data on the graph.
7. Increase the hanging mass to 2.0-g and lower the cart mass to 398-g. This will keep the
total mass accelerated to 400-g.
8. Repeat steps 3-6 until a total of 5.0 grams is used to accelerate the cart.
9. Continue collecting data. Each time moving 1-g of mass from the cart to the hanging
mass, yet keeping the total mass of the system at 400-g.
Record all measurements in the data table.
ANALYZING THE DATA
1. Calculate the net force acting on the cart for each trial. The net force on the cart
is the tension in the string caused by the weight of the hanging mass minus the
friction forces. If friction is neglected, the net force is:
Fnet = mg
2. Also calculate the total mass that is accelerated in each trial (M + m).
3. Graph the acceleration versus the applied net force for cases in the data table.
4. Calculate the theoretical acceleration using Newton’s Second Law (Fnet = ma).
Record the theoretical acceleration in the Data Table.
16
DATA TABLE:
Acceleration of a Cart - "Changing Net Force on Same Total System Mass"
Trial
Mass
Mass
of Cart hanging
(kg)
(kg)
1
(M)
0.399
(m)
0.001
2
0.398
0.002
3
0.397
0.003
4
0.396
0.004
5
0.395
0.005
Acceleration
Measured
(m/s2)
Applied Fnet
(N)
Total Mass
(Kg)
Fnet = mg
(M + m)
Acceleration
Calculated
(m/s2)
a = Fnet/(M+m)
PART 2:
Investigate the mass-acceleration relationship - "Same Applied Force on
different total system mass."
• Change the total mass, yet keep the net force the same as in one of your
first trials. Add mass to the cart, keeping the hanging mass (5.0-g) the
same. Follow the table as outlined below.
Trial
Mass of Mass
Cart
hangin
(kg)
g
(kg)
(M)
(m)
1
0.195
0.005
2
0.295
0.005
3
0.395
0.005
4
0.595
0.005
5
0.795
0.005
Acceleration
Measured
(m/s2)
Applied
Force
(N)
Total
Mass
(Kg)
Acceleration
Calculated
(m/s2)
( Fnet = mg)
(M+ m)
a = Fnet/(M+m)
QUESTIONS
1. What relationships exist between these variables as indicated by your data? Sketch a
graph of each of the following. (Hint: Read the "Theory" section of this lab and see if
your data supports it.)
a. acceleration vs applied Force
b. acceleration vs. total mass
17
2. Identify the independent, dependent and control variables in Part 1 and Part 2 of this lab:
Lab
Independent
Dependent
Control
Part 1
Part 2
3. How does the "measured" acceleration compare to the "calculated" acceleration?
4. What are some factors that could account for this difference?
5. If the force applied to a fixed mass is 6x greater, what would be the observed change in
the object's acceleration? _____________ If the force was 1/10 as great? ___________
6. If the force on an object is constant and the mass increased by a factor of 9x, what would
be the observed change in the object's acceleration? ___________ If the mass was 1/9 as
great? _______________
7. Why was the cart mass (M) and the hanging mass (m) added to determine the amount of
mass accelerated by the net force?
8. State Newton's Second Law in terms of Force, Mass and Acceleration without the use of
a mathematical formula.
18
9. In this virtual lab friction was negated (or a non-force acting on the system). What would
frictional forces do to the acceleration obtained by the "cart-weight" system?
10. What consequence would frictional forces have on the net Force (Fnet)?
12. Would Newton's Second Law of Motion (F = ma) still be correct with frictional forces
acting on the system? Justify your answer.
13. Go into Excel and plot a graph of measured acceleration vs. the ratio of Fnet/mass for all 10 of your data points
above. What is the slope of the line of best fit for your graph?
19
SPH3U: Force, Mass and Motion - Day 70 - OPTIONAL
In this investigation you will examine two factors that affect an object’s
motion: force and mass. To do this you will construct an Atwood
machine. You will need: a dynamics cart, a pulley, a C-clamp, string, a
tickertape timer, and a variety of masses.
Recorder: _________________
Tickertape
timer
Manager:
_________________
Speaker: __________________
0 1 2 3 4 5
m2
m1
The equipment is set up as shown in the beautiful diagram above. Complete all the following questions below
before beginning the experiment and show this page to your teacher. You need a clear understanding of what is
going on or else you may have to correct a lot of work!.
A: How the Atwood Machine Works
1. Ignore the tickertape timer for now. Explain why each mass, m1 and m2, will move when released. What
forces causes the acceleration of each mass?
2. When the weight, m1, is released how much mass is moving in total?
3. What single force is the ultimate cause of the motion of the whole system (m1 and m2 together)? This is the
force we will vary in our experiment.
4. To conduct a scientific investigation one must always change only one variable and measure the results while
ensuring everything else remains the unchanged. Suppose you want to increase the force moving the system
while keeping everything else the same. You add 200 g to m1. What else must you do?
5. Handy Trick! We will use the tickertape timers to measure acceleration. To avoid too much dot counting, we
will use a trick to quickly find the acceleration. The cart will start from rest, you can measure the
displacement and the time of the accelerating pattern of dots on the ticker tape. Choose a BIG 5 and show
how you can use it to find the acceleration.
20
B: Investigating the Effects of Force
In this first experiment you will vary the force while keeping all other properties constant, to determine the
effect of force on the acceleration.
1. Describe how you will conduct your experiment.
2. What is the total mass of your system (m1 + m2)? Remember, you must keep this constant!
3. Complete the chart and graph below to determine how force affects acceleration. Hint: make fairly large
changes in the masses (at least 200 g) and use a wide range of masses in order to see clear results!
m1 (kg)
m2 (kg)
Total Mass (kg)
Acceleration (m/s2)
Force (N)
5. Construct a graph of your
results and draw a line of best
fit. Note that force is given on
the vertical axis. This is done to
assist with our later
calculations.
Force (N)
4. Show a sample acceleration
calculation.
6. Use the pattern in your graph to
help explain how acceleration
depends on force.
Acceleration (m/s2)
7. Determine the slope of the graph including units. Show your work.
21
8. Is the value of the slope close to any other quantities which describe our system? What do you think the
slope physically represents about the object?
9. Write an equation for the line on your graph. Use symbols for force and acceleration.
10. If we double the force acting on the system, what will happen to the acceleration?
11. If we reduce the force to one third, what will happen to the acceleration?
12. Consider the graph above.
i) If the total mass of your system was greater, how would the graph appear different? What difference
in the motion would we observe?
ii)
If the total mass of your system was smaller, how would the graph appear different? What difference
in the motion would we observe?
iii) In general, how do you think an object’s acceleration depends on its mass, given a constant force?
C: Conclusions
1. Write a brief conclusion stating what general principle or concept this investigation has illustrated.
22
SPH3U: Newton’s Second Law Problem Solving – Day 70 cont’d
Many force problems combine both forces and motion. In such a problem there are a few things that we will add to
the “Given” step of our GRASS process:
 Attach the motion information to a motion diagram (dot pattern).
 Draw a free body diagram and list the force and mass information next to it.
Most questions involve both force and motion. Newton’s 2nd law is guaranteed to be involved, so Fnet = ma should be
the starting point of your “Approach” step.
1. Stopping a Neutron When a nucleus captures a stray neutron, it must bring the
neutron to a stop within the diameter of the nucleus by means of the strong force.
That force, which "glues" the nucleus together, is approximately zero outside the
nucleus. Suppose that a stray neutron with an initial speed of 1.4 x 10 7 m/s is just
barely captured by a nucleus with diameter d = 1.0 x 10-14 m (the stopping
distance). Assuming that the strong force on the neutron is constant, find the
magnitude of that force. The neutron's mass is 1.67 x 10-27 kg.
2. Sunjamming A "sun yacht" is a spacecraft with a large sail that is
pushed by sunlight. Although such a push is tiny in everyday circumstances,
it can be large enough to send the spacecraft outward from the Sun on a
cost-free but slow trip. Suppose that the spacecraft has a mass of 900 kg
and receives a push of 20 N. (a) What is the magnitude of the resulting
acceleration? If the craft starts from rest, (b) how far will it travel in 1 day
and (c) how fast will it then be moving?
3. Two People Pull Two people pull with 90 N and 92 N in opposite directions on a 25 kg sled on
frictionless ice. What is the sled's acceleration?
4. Take Off A Navy jet with a mass of 2.3 x 104 kg requires an
airspeed of 85 m/s for liftoff. The engine develops a maximum force of
1.07 x 105 N, but that is insufficient for reaching takeoff speed in
the 90 m runway available on an aircraft carrier. What minimum force
(assumed constant) is needed from the catapult that is used to help
launch the jet? Assume that the catapult and the jet's engine each exert
a constant force over the 90 m distance used for takeoff.
5. Loaded Elevator An elevator and its load have a combined mass of 1600 kg and
experience a force of gravity of 15680 N. Find the tension in the supporting cable when
the elevator, originally moving downward at 12 m/s, is brought to rest with constant
acceleration in a distance of 42 m.
6. Elevator An elevator with a mass of 2840 kg is given an upward acceleration of 1.22 m/s2 by a
cable. (a) Calculate the tension in the cable, (b) What is the tension when the elevator is slowing at the
rate of 1.22 m/s2 but is still moving upward?
Answers: 1. 16 N; 2. (a) 0.02 m/s2; (b) 8x104 km; (c) 2x103 m/s; 3. 8.0 cm/s2; 4. 8.2x105 N; 5. 1.8x104 N; 6. (a) 31.3 kN; (b) 24.4 kN
23
SPH3U: Forces as Interactions – Day 71
Recorder: _________________
Manager: _________________
Speaker: __________________
A: Truck vs. Car!
0 1 2 3 4 5
1. (Individually) Imagine a car and a truck push on one another or
collide. We want to explore the forces that arise in a few of these

situations. For each situation consider two possible forces: the force the truck exerts on the car, FT C , and the

force the car exerts on the truck, FC T . Decide based on the situation, whether each force is present and, if
both are, compare their magnitudes. When finished, record your results on the board.
Example
Exists?

FT C

FC T
Compare
(<, >, =)
a) A truck pushes a stalled car
from behind. They move together
at a constant velocity.
b) A fast moving car hits a truck
at rest.
c) A fast truck hits a car at rest.
d) A truck tows a car. They are
speeding up together.
2. Explain why, according to common sense, someone might decide that, in example (c), the truck exerts the
greater force.
B: Analysis - Kinematics
1. Explain why the dotted vertical lines correctly
represent the starting and ending moments of the
collision.
4
Velocity (m/s)
Consider the collision between a quickly moving truck
and a car at rest, example (c) from part A. We will
model this with a large and small dynamics cart (720
g, 360 g). To the right is a graph showing the v-t data
for each throughout the collision. The positive
direction is to the right.
3
Large Cart
2
Small Cart
1
0
0
0.1 Time (s) 0.2
0.3
2. What is the duration of the collision?
3. What is the evidence, according to the data, that the large cart experiences a force? What about the small cart?
4. Use the velocity information to find the average acceleration (including direction) of each cart during the
complete collision. Show all your work.
24
5. Which cart experienced the greater acceleration? Describe, in an intuitive way, why this seems reasonable.
6. Imagine these were vehicles in a collision. Which one would you prefer to be in? Explain.
7. Do the results from question B#4 support or contradict the explanation from question A#2? Offer your
opinion and move on.
C: Analysis - Forces
It is clear from the data and your calculations that the small cart reacts more during the collision – its acceleration
is the greatest. But this is not the end of the story. Acceleration is the result of force, and we have not yet found
the forces responsible. In this collision, the forces the carts exert upon one another are much larger than the force
of friction. Therefore it is reasonable to ignore friction and assume that there is only one important horizontal
force acting on each cart.

1. Draw a FBD for each cart showing the horizontal forces. Label the forces FL  S , meaning the force of the

large cart on the small cart, and FS  L , meaning the force of the small cart on the large cart.
2. Calculate the magnitude of the forces on your FBDs using your acceleration results. Watch the signs!


3. How does the magnitude of FL  S compare with FS  L ?
4. The force results seem like a contradiction of our common sense as explained in question A#2. Explain why
this is not a contradiction of our intuition.
5. Explain how forces of the same size produce such different acceleration results.
The case we have just studied is an example of a very general law about forces. When objects interact, a pair of
forces is always produced – they are really two parts of one interaction. Each object exerts a force upon the other.
These forces are simultaneous. They are the same type of force and the size, but are oriented in opposite
directions. Such a pair of forces is called a Newton’s Third Law force pair.
25
SPH3U: Newton’s Third Law – Day 71 cont’d
Recorder: _________________
Manager: _________________
Speaker: __________________
A: The Homework Stack
0 1 2 3 4 5
Two dusty textbooks are stacked on your bedroom floor. A heavy
biology text is on the bottom and a slender physics text is on the top.
1.
Draw a FBD for each text. Label each force showing the type and which object
exerts the force on which. For example,
Physics
Bugology
.
2. Rank the magnitudes of all the normal forces from least to
greatest (should be three!). Explain your reasoning.
3. Which of the forces in the two FBDs are third law pairs?
Identify any third law force pairs by drawing one or more
small “” symbols through each member of the pair. For
example, if you have two sets of third law force pairs in the diagrams, mark each member of the first pair as
, and each member of the second pair as
.
B: The Apple and the Earth
The story goes that Sir Isaac made a great discovery while he was sitting under an apple tree and an
apple happened fall down on him.
1. Draw a FBD for the apple while at rest on the ground. Label each force
showing the type and which object exerts the force on which. Identify any
third law force pairs.
Apple
2. A student says, “The two forces on the FBD must be third law pairs, they are
equal in magnitude and opposite in direction.” Do you agree or disagree?
Explain.
3. Draw a FBD for the apple and the earth while the apple
is falling. Label each force showing the type and which
object exerts the force on which. Identify any third law
force pairs.
4. A student says, “I think both the apple and the earth
should be accelerating.” Do you agree or disagree?
Explain.
26
Apple
Earth
5. A student says, “It is just not possible for the apple to exert a large force of gravity like the earth
does, and the earth clearly doesn’t move.” Do you agree or disagree? Explain.
6. The apple has a mass of 0.2 kg. What is the magnitude of the force of gravity it experiences? Explain
how we can find the resulting acceleration.
7. The earth has a mass of 6.0 x 1024 kg. What is the magnitude of the force of gravity it experiences?
Actually find the resulting acceleration.
8. Based on your results from question B#7, why is it understandable that most people think the apple
has absolutely no effect on the earth?
C: Physics on Ice
You have brought your little cousin out staking for the very first time. Both of you are standing on the
ice wearing skates (no friction) and are facing one another. Your little cousin is a bit timid and needs to
hold on to your scarf.
1. She holds on while you gently pull the scarf with a 6 N force to start her
moving. Her little mass is 17 kg. Draw a FBD for her and determine her speed
after pulling for 2.0 s.
Little Cousin
2. A student says to you: “I understand why the cousin speeds up – you are
pulling on the scarf and she holds on. But I don’t think you will move. Your
cousin is only holding on, not pulling. And, in any case, she is much smaller
so she couldn’t pull you anyways.” Do you agree or disagree? Explain.
You
3. Draw a FBD for you on the ice with your cousin. Use your actual mass to
determine your speed after the same 2.0 seconds of pulling.
27
Homework: Newton’s 3rd Law
1. A Child Stands Then Jumps A 29.0 kg child, with a 4.50 kg pack on his back, first stands on a
sidewalk and then jumps up into the air. Find the magnitude and direction of the normal force on the
sidewalk from the child when the child is (a) standing still and (b) in the air. Now find the
magnitude and direction of the net force on the earth when the child is (c) standing still and (d) in
the air.
(a)
(b)
(c)
(d)
2. Sliding Down a Pole A firefighter with a weight of 712 N slides down a vertical pole with an
acceleration of 3.00 m/s2, directed downward. What are the magnitudes and directions of the vertical
forces
(a) on the firefighter from the pole and
(b) on the pole from the firefighter?
3. Girl and Sled A 40 kg girl and 8.4 kg sled are on the frictionless ice of a frozen lake, 15 m apart but
connected by a rope of negligible mass. The girl exerts a continuous, horizontal force of 5.2 N on the
rope.
(a) What is the acceleration of the sled?
(b) What is the acceleration of the girl?
(c) How far from the girl’s initial position do they meet? (Hint: write an equation for xs and xg)
Answers: 1. (a) 328 N, down; (b) 0 N; (c) 0 N; (d) 328 N, up; 2. (a)
494 N, up; (b) 494 N, down; 3. (a) 0.62 m/s2; (b) 0.13 m/s2; (c) 2.6 m
28
SPH4U: Friction – Day 72
Recorder: __________________
Manager: __________________
Speaker: _________________
How does friction work? Let’s find out!
0 1 2 3 4 5
A: Looking for Friction in All the Right Places
For this activity you will need:
 1 wood block with hook
 1 spring scale (10 N range)
 bunch of masses
Attach your spring scale to a heavy object. Very gradually begin to pull on the object until it moves at a
slow, steady speed. Do this a few times until clearly notice when the object becomes “unstuck”.
1. Starting from zero, describe what happens to the readings on the spring scale as you very
gradually increase the force.
3. Sketch a graph showing the size of the force of friction
according to your scale readings as you gradually
increased the size of your force. Include both before
and after it starts moving.
Force of Friction
2. What happens to the object when you notice the sudden change of the spring scale reading?
Time
4. In which of the following situations does the object experience a force of friction? Draw a free
body diagram for the object in the three following situations:
a) at rest, you exert no forces b) at rest, you are starting to
c) moving at a constant
on it
pull
velocity due to your pull
29
5. Compare the size of the force of friction with the force you exerted in situations a, b, and c.
6. There are two kinds of friction: static friction for stationary objects and kinetic friction for
moving objects. Label the free body diagrams above as static or kinetic. Label your graph from
question 3 to show the static and kinetic friction regions.
7. When the object is at rest, what happens to the size of static friction as you very gradually
increase your pull? Try this with a heavy object.
B: How the Normal Force Affects Kinetic Friction
Kinetic friction arises when two objects are in contact and are sliding relative to one another. Being in
contact, they exert normal forces on each other. How does the size of the normal force affect the force
of kinetic friction?
1. On a horizontal surface how does the normal force compare with the object’s weight?
(Remember, weight = Fg = mg)
2. Using the equipment from the first part, devise an experiment, take data and plot a graph to
answer the question of Part 2. Explain your procedure for this experiment.
3. Write headings for your table, list your data (fill up the table!) and plot it on the graph.
30
4. Draw a free body diagram showing your block while you are pulling it. Under what condition
will your applied force be equal to the force of kinetic friction?
5. Describe in words the type of mathematical relationship between the Fn and Ffk.
6. Determine the slope of this graph. This value is called the coefficient of kinetic friction (k).
What characteristics of your experiment affect the size of the slope?
7. Does the mass of the object have any significant effect on the coefficient? Explain how you can
tell from your graph.
8. Make a prediction. What will the force of friction be if your mass weighed 400 N? 2 000 N?
9. Write down the equation for the line of best fit of your graph. Use the symbols Fn,  and Ffk.
C: How the Type of Materials Affects Kinetic Friction
1. Offer your opinion: What are some possible causes of friction between two surfaces?
2. Predict what kinds of surfaces will produce little friction and what kind will produce great
friction.
In the next activity you will investigate what combination of surfaces will produce the most friction.
Make sure that you use a clean surface, otherwise you will be measuring the forces from grinding
dirt. Draw the heavy friction box over four surfaces (lab table, glass, floor, one more of your choice).
Change the upper surface by attaching something like acetate (an overhead) to the box.
31
3. What is the mass of your block?
4. List all possible combinations of upper and lower surfaces. Predict which will yield high,
medium or low friction.
Bottom Surface
Upper Surface
Prediction
Force of
Coefficient
Friction (Ff)
(k)
5. Drag the loaded wood block over each surface and measure the force of kinetic friction. Attach
the acetate to the bottom of the block and drag the block over each surface. Record your results
in the chart. Remember to keep your surfaces clean!
6. Were there any surprising results? Can you offer any reasons why?
An important quantity for the discussion of friction is the coefficient of kinetic friction. This value
depends only upon the physical properties of the two surfaces and is found by the expression:
Ff = kFn
7. Calculate the coefficient of kinetic friction for the combination of surfaces in your experiment
and add these to the table.
32
Gravity - SPH 3UI - Day 73
Review - SPH 3UI – Day 74
Test - SPH 3UI - Day 75
33
SPH3U: Representing Forces and Motion – Day 74 (Review)
This activity presents four different situations. Your goal is to describe the forces and motion involved in each
using a variety of different representations. You will do this by completing the missing information in each box.
1
Picture and Description
Free Body Diagram
A car is being towed by a tow truck which exerts a horizontal
force. Both are speeding up after being stopped at a red light.
The car experiences friction .
Compare Forces
Net Force
horizontal:
(Fnet)x =
Motion Diagram
The car
Velocity-Time Graph
+
vertical:
(Fnet)y =
-
Description of Motion
2
Picture and Description
Free Body Diagram
A child pulls a wagon along the sidewalk at a steady speed.
The handle is level with the ground. There is a large dog
sitting in the wagon.
Compare Forces
Net Force
horizontal:
(Fnet)x =
Motion Diagram
The wagon only
Velocity-Time Graph
+
vertical:
Description of Motion
34
(Fnet)y =
-
3
Picture and Description
Free Body Diagram
The woman
A woman rides in an elevator that is slowing down after
traveling up to the 16th floor of her apartment building.
Compare Forces
horizontal:
Net Force
(Fnet)x =
Motion Diagram
Velocity-Time Graph
+
vertical:
(Fnet)y =
-
Description of Motion
4
Picture and Description
Free Body Diagram
The car.
A group of friends is pushing a heavy stalled car, slowing it
down as it rolls on a level driveway. It experiences friction.
Compare Forces
horizontal:
Net Force
(Fnet)x =
Motion Diagram
Velocity-Time Graph
+
vertical:
(Fnet)y =
-
Description of Motion
35
SPH3U: Physics Idol!
Group Members: ______________________________________________________________________________________
Physics Topic:________________________________________________________________________________________
Desperate for fame, you and a group of your colleagues have decided (yes, you have) to enter this year’s Physics Idol
competition! Choose a topic or problem from the unit on forces, create a song or video that explains it and submit your work
to the judges (your teacher) and wait for the lucrative career opportunities to roll in!
Criteria - The judges will be looking for:
 An in depth understanding of a physics concept or problem from the force unit
 The song lyrics should be between two to four minutes long (guitar solos don’t count!)
 The video should be between three and four minutes long
 All lyrics and script for the video must be appropriate for a classroom (no foul language, etc.)
 You may work individually, or in a group of two or three
Hand-in
 A CD or mp3 with your song; or a DVD or WMV (windows media video format) compatible file
 Alternately, instead of submitting a CD or mp3, the song may be performed live in class
 A simple handout with your lyrics to the song or the script for the video
 This evaluation page (an extra copy can be printed out from the course website if needed)
Length
Creativity
Delivery /
Presentation
Organization
Content
Evaluation
Level 1
States few main points
and details that focus on
the topic or information
does not relate to topic.
Level 2
States most of the main
points and details that focus
on the topic. May include
some unnecessary
information.
Level 3
Adequately states the
main points and details
that are accurately focused
on in the topic
Little or no attempt is
made to stay on the topic
or follow a logical flow
of information.
Presentation is not well
organized or deviates far
from intended topic.
Does not consider
audience. Difficult to
understand / follow.
Presentation is lacking in
preparation and in
practice of the delivery
including voice, pacing
and little or no use of
pictures. Difficult to
hear. (voice, posture, eye
contact, gestures, pacing)
Delivers the information in
a fairly logical manner but
does not stay on the topic.
Little consideration of
audience. Some
information was peripheral
to the project or use of
incomplete thoughts/ideas.
Adequately delivers the
information in a logical
sequence while staying on
the topic and considering
the audience. Speaks
clearly and confidently
about topic. Information
was covered in a
satisfactory manner.
Effectively and creatively
delivers the information in a
logical sequence while
staying on the topic and
considering the audience.
Interesting and vivid to hear
and/or watch.
Presentation shows some
preparation as well as some
practice in the delivery
including marginal use of
voice, pacing and pictures.
(voice, posture, eye contact,
gestures, pacing)
No real original
presentation ideas; does
not engage audience.
Little original content; little
engagement with audience.
Mostly presented facts
without engagement
Presentation shows
satisfactory preparation as
well as practice in delivery
including use of voice and
pacing. Some use of
pictures, graphics, skits
and real life media. (voice,
posture, eye contact,
gestures, pacing)
Some original content;
some taking advantage of
audience’s attention and
maintaining interest.
Presentation shows detailed
preparation and practice in
delivery including use of
voice, pacing and the use of
pictures, graphics, skits, real
life media etc. Interesting
and vivid. (voice, posture,
eye contact, gestures,
pacing)
Original presentation; takes
advantage and holds
audience’s attention.
Within +/- 1 minutes of
allotted time
Within +/- 30 seconds of
allotted time
Within the allotted
time
Within +/- 2 minutes of
allotted time
Level 4
Thoroughly and clearly
states the main points and
precise details of the topic.
/10
/5
/5
/5
/5
Total
36
Marks
/30